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A gamma integral

  1. Apr 7, 2012 #1
    greetings . any ideas on how to evaluate this integral

    [tex] \lim_{T\rightarrow \infty}\frac{1}{2T}\int_{-T}^{T}\frac{\Gamma(3+it)}{\Gamma(3+it-j)}e^{ikt}dt[/tex]

    [itex] j, k [/itex] are positive constants .
  2. jcsd
  3. Apr 8, 2012 #2
    Hi !
    this integral cannot be evaluated for T-->infinity because it is not convergent.

    Attached Files:

  4. Apr 8, 2012 #3


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    The gamma function ratio is a polynomial in t (degree = j, if j is an integer).
  5. Apr 8, 2012 #4
    Not sure, but would a fourier transform help here?
  6. Apr 9, 2012 #5
    I don't think so. Since the integral is not convergent for T tending to infinity, the Fourier transform is of no help to find a limit which doesn't exist anyways.

    This is a so-called Pochhammer polynomial.
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